• Pablo Ziffer

Other Harmony, From Total Harmony to Combinatorial Harmony




Franck Jedrzejewski: From Total Harmony to Combinatorial Harmony Historical reflections of harmony beyond tonal and atonal via Johnson's examples of Euler, Obouhow, Hauer, Slonimsky, Schillinger and Messiaen, and some others. From Edmond Costere Affinity tables to the new list of Homometric multiplets that I compute, and used by Stéphane de Gerando, I will try to understand what remains or what musical harmony means today. Tom Johnson: Other Harmony Hundreds of harmony books have been devoted to tonality, and many have dealt with atonality, which has usually meant serialism, but this book considers all of the Other Harmony that has dominated musical practice for at least 50 years. After considering theories of Forte, Euler, Hauer, Slonimsky, Obouhow, Schillinger, and Messiaen, the book considers some of my own harmonic practices having to do with heights, sums modulo n, homometric pairs and combinatorial designs. I will do my best to summarize the Important points in all this, playing some musical examples, and to talking about some of the questions I still have. Emmanuel Amiot : Tom Johnson l'exhaustif La collaboration entre le compositeur Tom Johnson et le monde mathématique est étonnament longue et fructueuse. Elle ne peut s'expliquer simplement par l'étiquette de "minimaliste" qui lui est attachée, car pour la plupart des autres compositeurs de cette mouvance le rapport aux mathématiques est bien plus ténu. Je tenterai d'explorer plutôt des convergences de pensée, de méthodes, d'objectif, en m'appuyant notamment sur son dernier ouvrage Other Harmony.



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